Way to authenticate a users on two different systems

I have two web applications

1. Logger; comes with a desktop app
2. Workflow tool

Workflow tool has all the users, which I have imported into Logger.

The problem that I am faced with is that Logger and Workflow tool use different hashing methods for passwords, due to which users who use workflow tool ain't gonna be able to access Logger with their current login details.

At the present moment, the only solution that I have is extending authentication method within the Logger, with the ability to define which hashing method Logger should use for the particular user. However, I am looking to integrate Logger with some other different tools and it could be a lot of hassle for myself to set up different hashing for different tools, but it might be my only way forward...

Reason for this questions is because I would like to know if there is a better solution then I have come up with above.

Note about Workflow tool; the system is using one-way hashing mechanism and has no API in place.

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Logger is written in the Laravel 5.1; for my solution, I would require extending Laravel's built-in authentication method.

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